What doctor do you see for red veins on your eyelids?

Laser specialist. There are dermatologists and ophthalmologists who specialize in treatment of veins of the eyelids using certain lasers. Treating the upper eyelids with lasers usuallly requires special protective eyeshields that are placed inside the eye along with a protective lubricant and numbing drops. Very important to make sure the doctor is highly experienced and trained to perform these treatments.
Cosmetic Surgeon. If you have noticeable blood vessels on your face and eyelids you may benefit from seeing a dermatologist, or plastic surgeon that is trained in cosmetic & laser surgery. What you have can most likely be treated with 1-2 treatments using a vascular laser.